Express K#S^2#T#2P as a connected sum of projective planes or as a connected sum of tori.

Q: Compute Div(F) and Curl(F): F--(4y-1) i+yj+(-3y) k

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Q: 2. An is a set of points (x, y) in a plane such that the sum of the distances between (x, y) and two…

A: We know that, The sum of distances to any point on the ellipse x,y from the two foci c,0 and -c,0 is…

Q: SEr up AN INTEGNAL KEPRESENTAT7 ON OF THE ARGA OFTHE REFGrON BOUNDEO BY y =x3,y=0, x=-l, X= 2 ド

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Q: az az and at the point (-1, -3, -2). Suppose ry z - 94 = 4xy – z. Compute ду dz |(-1,–3,–2) az…

A: An important result from advanced calculus, called the Implicit Function Theorem,states the…

Q: Discuss the Singulazities and Poles of fiz) = zéSinz (z-2) (zこいこょうと+ら)(2t (こか) +4

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Q: Compute Ax by dot product. 2 10 1 2 1 0 0 1 0 0 1 2 1 2 1 1 2

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Q: The fourth left-endpoint in a partition of [0, 3] with Ax = 0.5 is

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Q: Let S in Mzx2; a + 2d=0 and b-2c 0 with the standard %3D operations in M2x2 Which of the following…

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Q: EX: Show that the telation ? >' is PartiaL oldering set of Por R-

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Q: find all the Second order partial denvatives of the givén funcion fua、り) %3D

A: The given function is f(x,y)=exy

Q: Y Show that f (2)= 2+ Con formal maps %3D on %3D

A: Given that,f(z)=z+1zz=1

Q: Construct a clamped cubic spline passing through the points 9, 13 and 22 with fx=x3+1

A: f(x)=x3+1y0=f(9)=730y1=f(13)=2198y2=f(22)=10649 Here h0=4h1=9 For given set of points (x, y) that is…

Q: 23. Prove that (xo, Yo), (x1, y1), and (x2, y2) lie on a line if and only if (х — Хо)02 — Уо) - (*з…

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Q: Type here to search Check 2. %3D D = (-) + *** - ,(-) + ,(+-) + (+-)

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Q: Use Theorem 2.4.1 to prove that f(x,y) = 1 - x^2 - y^2 defined in R^2 is concave.

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Q: show that (0.1)with usual topology is connected

A: Sol

Q: Which elements are invertible in Z4[x,y]?

A: W need to find elements which are invertible inZ4x,y.

Q: mple. Compute AB and BA where 1 -1 A = %3D B = -2 2 3 4

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Q: Compute x 2z ds where C is the line segment C from (0,6,–1) to (4,1,5).

A: The given line segment from   to   can be represented parametrically as: , , and , for    Using the…

Q: Verify the Cauchy-Schwarz Inequality for u = (1, −1, 3) and v = (2, 0, −1).

A: u = (1, −1, 3) and v = (2, 0, −1) To verify the Cauchy-Schwartz Inequality for the given set of…

Q: If after evaluating the Wronskian of the functions y1 and y2 the result is W=7x2+19 in the interval…

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Q: A 6x 6 square is tiled by 2x 1 dominoes. Prove that it has at least one fault-line, that is, a…

A: Consider a 6×6 square which is tiled by 2×1 dominoes. Suppose the 6×6 square has no fault lines.…

Q: dz Let z-ay" – 4r, * = uv and y-v - 3u. Compute Ən (u,r)-(1,1) -

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Q: 5. Evaluate f (x²zdx – yx²dy + 3dz) where C is the boundary of the triangle with vertices (0,0, 0),…

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Q: Compute ∇ƒ(-1, 2, 1), where ƒ(x, y, z) = xy/z.

A: Given,f(x,y,z)=xyz     As we know ∇f(x,y,z)=∂f∂x,∂f∂y,∂f∂z

Q: 2. Find three positive integers x, y, and z if their product is 27 and the sum is a minimum.

A: Given three positive numbers are  x, y, and z Product = xyz = 27 And sum is minimum

Q: graph the inequality on a coodinate plane x > with line under it 2

A: To graph the given inequality x≥2.The equation x=2 has a graph that is a vertical line with all…

Q: Let w = -4xy – 5yz – 4xz, x = st, y = et, z = t Compute (3,4) = as (3,4)%3D at

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Q: Verify that (AB)" = BT AT %3D التحق ق 3 2 4 2 1 3 A = 2 1 B =1 2 5 4 2 3 0 2 1

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Q: If C, C2 Cn are Constovts 1-1 . a,, uzXz) ---- Un (X)ave livffen antiable 4111 funetions at x with…

A: Introduction: The differentiation of a function y=fx is defined as f'x=limh→∞fx+h-fxh This is…

Q: Compute ƒxz and ƒzz for ƒ(x, y, z) = xyz - x2 z + yz2.

A: Given that f(x,y,z)=xyz-x2z+yz2. We need to find : i)fxz. ii)fzz.

Q: Let f be q functiom that admits contırous second partial denvatives Df (X.Y)=(4x²- 2q²x+ 2q°y ,4y³ +…

A: Given, the second partial derivatives              ∇f(x, y)=4x3-2a2x+2a2y,  4y3+2a2x-2a2ywith a>0

Q: Theorem 3. Every solution of Eq.(1) is bounded if a + < 1.

A: As per the information, we will first find a recurrence relationship of the sequence, then find its…

Q: 1- -Н(y)-Н(yх) Prove that 2- H(x,y) = H(y) + H(x\y) 3- H(x,y) = H(x) + H(y}x) 4- Н(х., у) %3DН(х) +…

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Q: 3. Compute fc F · dr where F(x, y, z) = (x+ yz, 2x, xyz) where C consists of the segments from (1,0,…

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Q: Find the bounded อน əx solution of อน 2 + U if U(x, 0) = 6e-3x. at

A: We have ∂u∂x=2∂u∂t+u  The initial condition is ux,0=6e-3x Now, ∂u∂x=2∂u∂t+u can be written as…

Q: Can you show an example of Null space?

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Q: Evaluate ff xydxdy over the square with corners (0,0), (1,1), (2,0) and (1, –−1) (u + v) (u - v) 2 2…

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Q: Let S = {2x, 1 –- x, x2 + x- 1, x + 1}. Then S is a %3D

A: for a basis we need to check that a set must be linearly independent and spans the whole vector…

Q: Suppose the operators Å and B are projection operators. Show that the sum of two projection…

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Q: 9. verify that lx1l= max ilt)| defines. telasb] a on the Space Ccla, b]. morm Solution :-

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Q: Find the bounded of the determine red In the same way as the proof of theorem 4 in the second…

A: Given:                                            Sn+1=Sn-paSn-q+bSn-r+cSn-sdSn-q+eSn-r+fSn-s…

Q: Find ß so that {1, x, 1+ 6x²) on (-1,1) is orthogonal.

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Q: If C, Cz - Cn are Constovts 2111 . u,), uzX2) ---- Un (X)ave Livffen antiable 4111 funetions at x…

A: Introduction: Differentiation is a property of a real-valued function. When the independent variable…

Q: Suppose div(F(5,3,2)) = 240. Estimate the flux of F out of a small, outward-oriented box of side…

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Q: How many points and lines does a finite projective plane of order 7 have?

A: The number of points in a projective plane of order n is n2+n+1. The number of lines in a projective…

Q: A sequence (a1, b1), (@2, b2), (a3, b3), -· - - of points in the co- ordinate plane satisfies (am+1;…

A: A sequence a1,b1,a2,b2,a3,b3,... of points in the coordinate plane satisfies the equation…

Q: -. Show that both R and R2 may be covered by countably many open balls.

A: Soution.

Q: Theorem. A rectangle R with side lengths 1 and x, where x is irra- tional, cannot be “tiled" by…

A: Without using the concept of linear algebra you can proof this. Let length of rectangle= 1 Unit…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.